A data dimension reduction method based on a tensor global-local preserving projection

Abstract

A data dimension reduction method based on a tensor global-local preserving projection comprises the following steps: (1) data samples are selected to form a sample set which is to be subjected to dimension reduction; (2) distances between sample pairs are calculated; (3) neighborhoods of sample points are divided to obtain close neighbor points and non-close-neighbor points; (4) neighboring right matrixes and non-neighboring right matrixes are established according to close neighbor relations and not-close-neighbor relations among the samples; (5) An object function corresponding to data global and local structure preserving is established, and an optimization problem is constructed; (6) the optimization problem is converted to a generalized eigenvalue problem, and a projection matrix is obtained through solving the problem; and (7) projection is carried out on the sample set to obtain dimension reduction data. Targeting at a dimension reduction problem of second order tensor data, the invention provides the data dimension reduction method which can simultaneously carry out excavation on the global and local structures of the data, which is good in dimension reduction effects and which are based on the tensor global-local preserving projection.

Description

technical field [0001] The invention relates to the field of pattern recognition and machine learning, in particular to a data dimensionality reduction method based on tensor global-local projection. Background technique [0002] In today's information age, thanks to the rapid development of data acquisition and data storage technologies, high-dimensional data has emerged in many fields, such as climate data, genetic data, remote sensing data, financial data, and voice, image, and text data. Some of the data are not only high-dimensional, but also high-order, that is, each data sample has a high-order tensor (second order or above) structure, such as an image dataset composed of multiple images. Data dimensionality reduction refers to reducing data from high-dimensional to low-dimensional according to certain criteria, eliminating data redundancy, and obtaining low-dimensional equivalent expressions of data characteristics, so as to detect the essential laws of data. At pre...

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Problems solved by technology

[0005] In order to overcome the shortcomings of the existing tensor data dimensionality reduction methods that only focus on the global structure or local structure of the data and have poor dimensionality reduction effects, the present invention provides a method that can simultaneously mine the global and local structure of the data and has a good dimensionality reduction effect. Data Dimensionality Reduction Method Based on Tensor Global-Local Preserving Projection

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